They had written the songs celebrating Ali Abdullah Saleh's departure many days before. On Sunday, as they partied in the square that has become the heart of Yemen's revolution, the people of Sana'a were finally able to sing them.

Speakers were cranked up to full volume as people danced and flew flags with the words "New Yemen" emblazoned upon them.

After 33 years of rule, Saleh left Sana'a on Saturday to seek medical treatment in Saudi Arabia. He had been injured in an attack on a mosque in his presidential compound. Many believe he will not come back.

Around 10,000 people gathered in the public space the protesters have dubbed Change Square. Beef stew was handed out by organisers and 40 cows were prepared for slaughter, a Yemeni tribal tradition to honour happy occasions.

"I am so happy," said Aum Ayah, a young woman who joined the festivities. "Finally we can find justice in this country. I hope that the youth in Change Square will work to find a good person to be the president of Yemen who cares about Yemen and treats the Yemenis well."

A wounded man and two blind men danced by the stage in the square. A traditional wedding song, in which the bride leaves her father's house for ever and is no longer welcome, was adapted as a satirical joke aimed at the president.

Women in black veils joined demonstrators carrying banners that hailed Saleh's departure. One read: "The oppressor is gone, but the people stay."

Activist and rights lawyer Khaled al-Ansi said families and children were arriving in the square in party clothes. "People have trickled in since dawn to the square. Some have not slept yet. It is like a holiday," he said.

In the heat, playful water fights broke out and children wore T-shirts bearing the red, white and black national flag of Yemen while others used face and body paints. Several people were carrying circular loaves of bread with "New Yemen" baked into them.

More women came out than during earlier stages in the protest. They seemed more animated than the men, many of whom had been up all night partying and chewing qat, which was available from a burgeoning number of vendors who have cropped up in the square. In the afternoon, some tents on the square were full of men sleeping. "Who would have believed that this people could have removed the tyrant?" said 30-year-old teacher Moufid al-Mutairi.

But there was also an undercurrent of anxiety that the revolution is not yet complete. Protesters set off fireworks throughout the day, only pausing for prayers at 12.30pm and 3.30pm. With a lack of information about whether Saleh's sons, who command well-resourced military brigades, were still in the country, some of the protesters were spooked by the bangs, fearing it was gunfire, and there were fresh clashes.

Some claimed they had been threatened with attacks by Saleh supporters in retribution for the injuries to the president. The fact he was attacked in his mosque has made them even angrier, they said.

Sheikh Abed al-Swatti, a tribal leader, told the Guardian: "My friends in the hospital who checked the president told me that he is seriously injured and that the shrapnel entered from his elbow and was 7cm away from his heart. One of his sons, Khalid, was seriously injured and his situation has not allowed him to be transferred to Saudi Arabia. King Abdullah has called Sheikh Sadiq al-Ahmar and they decided a truce for a week between the al-Ahmar and Saleh's loyal military."

"The revolution did not reach its aim yet," said MC Khaledz, a 17-year-old rapper in Change Square. "We didn't want to murder the president as we are peaceful protesters. We only wanted him to step down. It would be a huge mistake if he was killed. We should not think out of hatred and we shouldn't forget that this man in his early days did some good things for Yemen. His biggest mistake was that he opened the doors for corruption. Now the youth revolution should start. They shouldn't leave the square, they should stay and fight until all their demands are met."

Amar Merza, 23, from Hodida in the north of the country, said the revolutionaries were on their guard because Saleh remained "an unpredictable guy".

"We are so happy all of us today that Saleh has left, but there is a big concern that we should pay attention to that the president might come back," he said. "Although the possibility of him coming back is so small, some of the youth protesters have discussed what they could do if he returns. We already have a plan, but we don't want to reveal it now. Youth has to be a partner in the political situation, not only observing from outside. We should never forget our aim of creating a civil state [rather than a tribal system]."

Waheed Ahmed, 51, from Aden added: "Our demand was to overthrow the regime. We haven't reached that yet but we have decapitated it. We still need civil governement and we need elections as soon as possible because Yemen is ready."

"From the first day we will learn to be brothers," said Mohammed Abdulrahman, 60. "It doesn't matter what party you support or what city you come from, we are all Yemenis. If Saleh died that won't be good for our revolution. We want him to be prosecuted for all the blood that we lost in the revolution, for everything that happened to us, he is the one that is responsible. No matter his health situation now, he should be brought back and prosecuted."

'New leader'

Yemen's vice-president and acting leader, Abd al-Rahman Mansur al-Hadi (pictured above), is considered a political lightweight, a non-charismatic and shadowy figure who enjoys little support inside or outside the military – always a powerful player in Yemen's volatile politics.

Hadi has military experience, having received training in the UK, Egypt and Russia, but is said to have little clout and was promoted to vice-president as a gesture to the south.

"He is irrelevant, a token southerner," said one western expert on Yemen. "He is in charge according to the constitution but not in reality." Hadi's first task will be to open talks with opposition groups to try to settle the current crisis.

Although from the south – he was born in 1945 in al-Wade' district in Abyan governorate –, he defected with his unit to north Yemen following the bloody struggle in former Marxist south Yemen. He was rewarded for his role in the 1994 civil war between the north and the south by being appointed first minister of defence and then as vice-president. He graduated in 1964 from the Aden military school, before undergoing his international training.Khaled Fattah

Yemen TV denies reports on al-Jazeera that President Ali Abdullah Saleh's family have fled the country with him to Saudi Arabia, while opposition protesters celebrate Saleh's departure in al-Taghyeer Square